PVA of the NBI: GLM of survival and reproduction probabilities
- Hypothesis: We hypothesize that at the present time the northern bald ibis population can survive without further management and release. We predict that the observed demographic rates will ensure population growth and do not differ between the breeding colonies.
- Study area: Austria, Germany and Italy
- Data: Data of the mean per scenario for the first NetLogo model
In this script, we created GAMs and GLMs to find out whether survival per stage or reproduction probabilities have a significant effect on lambda.
Setup
## for non-CRAN packages please keep install instruction
## but commented so it is not run each time, e.g.
# devtools::install_github("EcoDynIZW/template")
## libraries used in this script
## please add ALL LIBRARIES NEEDED HERE
## please remove libraries from the list that are not needed anymore
## at a later stage
library("effects")## Loading required package: carData
## lattice theme set by effectsTheme()
## See ?effectsTheme for details.
## Loading required package: splines
## Loading required package: foreach
## Loaded gam 1.20
## here() starts at C:/Users/sinah/Documents/IZW/Drenske_2020_PVA_NBI
## Loading required package: nlme
## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.
##
## Attaching package: 'mgcv'
## The following objects are masked from 'package:gam':
##
## gam, gam.control, gam.fit, s
## Warning: package 'plot3D' was built under R version 4.0.5
## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --
## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.3 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.0
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x purrr::accumulate() masks foreach::accumulate()
## x dplyr::collapse() masks nlme::collapse()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x purrr::when() masks foreach::when()
Management improvement scenarios
## [1] 0.53 0.58 0.66 1.06 1.41 3.97
Change the column names
Add columns for survival
df_sc_mean$s1 <- (1 - df_sc_mean$m1)
df_sc_mean$s2 <- (1 - df_sc_mean$m2)
df_sc_mean$s3 <- (1 - df_sc_mean$m3)
df_sc_mean$s4 <- (1 - df_sc_mean$m4)Mortality and respective survival
## [1] "m1 vs s1"
##
## 0.2 0.3 0.36
## 108 108 110
##
## 0.64 0.7 0.8
## 110 108 108
## [1] "m2 vs s2"
##
## 0.08 0.19 0.26
## 108 108 110
##
## 0.74 0.81 0.92
## 110 108 108
## [1] "m3 vs s3"
##
## 0.14 0.24 0.31
## 108 108 110
##
## 0.69 0.76 0.86
## 110 108 108
## [1] "m4 vs s4"
##
## 0.02 0.14 0.22
## 108 108 110
##
## 0.78 0.86 0.98
## 110 108 108
Explore database
## [1] "Scenario" "Run" "Year" "IndAll" "IndB" "IndK" "IndUb" "IndFP" "IndP"
## [10] "IndBFP" "IndBP" "IndKFP" "IndKP" "IndUbFP" "IndUbP" "IndJuv" "IndSub1" "IndSub2"
## [19] "IndAdu" "m1" "m2" "m3" "m4" "RR" "N_Supplements" "Supplement_Time" "Stoch_Frequency"
## [28] "Stoch_Severity" "N_Juveniles" "N_Subadults1" "N_Subadults2" "N_Adults" "Lambda_sto" "SD_Lambda" "Extinct" "s1"
## [37] "s2" "s3" "s4" "pext"
View(df_sc_mean) # okay, these are mortalities.
unique(df_sc_mean[,c(20:24)]) # m1, m2, m3, m4, RR values per scenario## # A tibble: 326 x 5
## m1 m2 m3 m4 RR
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.2 0.08 0.14 0.02 0.53
## 2 0.2 0.08 0.14 0.02 0.580
## 3 0.2 0.08 0.14 0.02 0.66
## 4 0.2 0.08 0.14 0.02 1.06
## 5 0.2 0.08 0.14 0.14 0.53
## 6 0.2 0.08 0.14 0.14 0.580
## 7 0.2 0.08 0.14 0.14 0.66
## 8 0.2 0.08 0.14 0.14 1.06
## 9 0.2 0.08 0.14 0.22 0.53
## 10 0.2 0.08 0.14 0.22 0.580
## # ... with 316 more rows
## [1] 0.80 0.70 0.64
## [1] 0.92 0.81 0.74
## [1] 0.86 0.76 0.69
## [1] 0.98 0.86 0.78
## [1] 0.53 0.58 0.66 1.06 1.41 3.97
##
## 0 0.01 0.02 0.03 0.06 0.24
## 316 4 3 1 1 1
# 0 0.01 0.02 0.03 0.06 0.24
# 316 4 3 1 1 1
# Comment: Only in 10 out of 326 scenarios did the population ever go extinct.
# With such a distribution of the response variable,
# there is no need to calculate a model.
# Therefore we have described the distribution of survival and reproduction values
rows_ext_scen <- which(df_sc_mean$pext > 0)
ext_scen <- df_sc_mean[rows_ext_scen,]
ext_scen## # A tibble: 10 x 40
## Scenario Run Year IndAll IndB IndK IndUb IndFP IndP IndBFP IndBP IndKFP IndKP IndUbFP IndUbP IndJuv IndSub1 IndSub2 IndAdu m1 m2 m3 m4 RR N_Supplements
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.20.26~ 10451. 24.9 47.4 0 0 0 0 41.3 0 0 0 0 0 0 0.728 11.7 8.67 26.3 0.2 0.26 0.31 0.22 0.53 0
## 2 0.30.19~ 17651. 25.0 42.7 0 0 0 0 36.6 0 0 0 0 0 0 0.727 9.65 7.83 24.5 0.3 0.19 0.31 0.22 0.53 0
## 3 0.30.26~ 21250. 24.9 31.7 0 0 0 0 25.8 0 0 0 0 0 0 0.729 7.37 5.51 18.1 0.3 0.26 0.31 0.22 0.53 0
## 4 0.30.26~ 21351. 25.0 41.4 0 0 0 0 35.5 0 0 0 0 0 0 0.727 9.98 7.43 23.3 0.3 0.26 0.31 0.22 0.580 0
## 5 0.360.1~ 27250. 25 42.9 0 0 0 0 36.7 0 0 0 0 0 0 0.725 9.18 7.46 25.5 0.36 0.19 0.24 0.22 0.53 0
## 6 0.360.1~ 28451. 24.9 31.9 0 0 0 0 26.0 0 0 0 0 0 0 0.730 6.90 5.71 18.6 0.36 0.19 0.31 0.22 0.53 0
## 7 0.360.1~ 28551. 24.9 42.1 0 0 0 0 36.1 0 0 0 0 0 0 0.727 9.52 7.76 24.1 0.36 0.19 0.31 0.22 0.580 0
## 8 0.360.2~ 30851. 24.9 34.2 0 0 0 0 28.2 0 0 0 0 0 0 0.729 7.51 5.69 20.2 0.36 0.26 0.24 0.22 0.53 0
## 9 0.360.2~ 50051. 24.3 21.4 0 0 0 0 15.6 0 0 0 0 0 0 0.750 4.84 3.54 12.3 0.36 0.26 0.31 0.22 0.53 0
## 10 0.360.2~ 32151. 25.0 29.8 0 0 0 0 24.1 0 0 0 0 0 0 0.727 6.90 5.21 17.0 0.36 0.26 0.31 0.22 0.580 0
## # ... with 15 more variables: Supplement_Time <dbl>, Stoch_Frequency <dbl>, Stoch_Severity <dbl>, N_Juveniles <dbl>, N_Subadults1 <dbl>, N_Subadults2 <dbl>, N_Adults <dbl>,
## # Lambda_sto <dbl>, SD_Lambda <dbl>, Extinct <int>, s1 <dbl>, s2 <dbl>, s3 <dbl>, s4 <dbl>, pext <dbl>
##
## 0.2 0.3 0.36
## 1 3 6
##
## 0.19 0.26
## 4 6
##
## 0.24 0.31
## 2 8
##
## 0.22
## 10
##
## 0.53 0.58
## 7 3
# We can see that the highest mortality of adults was part of all scenarios where the population went extinct
# See also the excel file under "output\data-proc\model-proc\08_PVA_GLM_table_ext_scen.xlsx"# Explore lambda for s1 and RR
x <- df_sc_mean$s1
y <- df_sc_mean$RR
z <- df_sc_mean$Lambda_sto
scatter3D(x, y, z, pch = 19, cex = 0.7, clab = c("Lambda"), xlab = "s1", ylab = "RR", zlab = "Lambda")# Explore lambda for s4 and RR
x <- df_sc_mean$s4
y <- df_sc_mean$RR
z <- df_sc_mean$Lambda_sto
scatter3D(x, y, z, pch = 19, cex = 0.7, clab = c("Lambda"), xlab = "s4", ylab = "RR", zlab = "Lambda")GAM
A general additive model (GAM) tests for non-linearity
The extinction probability is the response variable and the predictor variables are formed by the survival probabilities per stage (s1-s4) and the reproduction (RR)
Response = Lambda
## Lambda and survival
gammod_2_1 <- gam(formula = Lambda_sto ~ s(s1, k=myk) + s(s2, k=myk) +
s(s3, k=myk) + s(s4, k=myk) +
s(RR, k=myk),
data = df_sc_mean,
na.action = 'na.fail', family=Gamma)
summary(gammod_2_1) ##
## Family: Gamma
## Link function: inverse
##
## Formula:
## Lambda_sto ~ s(s1, k = myk) + s(s2, k = myk) + s(s3, k = myk) +
## s(s4, k = myk) + s(RR, k = myk)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9036404 0.0004053 2229 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(s1) 1.000 1.000 964.7 <2e-16 ***
## s(s2) 1.000 1.000 887.0 <2e-16 ***
## s(s3) 1.000 1.000 893.8 <2e-16 ***
## s(s4) 1.908 1.991 5617.9 <2e-16 ***
## s(RR) 1.999 2.000 5328.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.985 Deviance explained = 98.6%
## GCV = 6.6955e-05 Scale est. = 6.5312e-05 n = 326
# F values for s4 and RR are very high - they have the highest influence
## Lambda and mortality
gammod_2_2 <- gam(formula = Lambda_sto ~ s(m1, k=myk) + s(m2, k=myk) +
s(m3, k=myk) + s(m4, k=myk) +
s(RR, k=myk),
data = df_sc_mean,
na.action = 'na.fail', family=Gamma)
summary(gammod_2_2) ##
## Family: Gamma
## Link function: inverse
##
## Formula:
## Lambda_sto ~ s(m1, k = myk) + s(m2, k = myk) + s(m3, k = myk) +
## s(m4, k = myk) + s(RR, k = myk)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9036404 0.0004053 2229 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(m1) 1.000 1.000 964.7 <2e-16 ***
## s(m2) 1.000 1.000 887.0 <2e-16 ***
## s(m3) 1.000 1.000 893.8 <2e-16 ***
## s(m4) 1.908 1.991 5617.9 <2e-16 ***
## s(RR) 1.999 2.000 5328.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.985 Deviance explained = 98.6%
## GCV = 6.6955e-05 Scale est. = 6.5312e-05 n = 326
Plots
vis.gam(gammod_2_1, view = c("s4", "RR"), plot.type = "persp", type = "response", zlim = c(0.5,1.8),
ticktype = "detailed", border = NA, n.grid = 1000, nticks = 3,
xlab = "s4", ylab = "RR", zlab = "Lambda",
color = "heat", theta= -140, cex.lab = 3, cex.axis = 2.5)vis.gam(gammod_2_2, view = c("m4", "RR"), plot.type = "persp", type = "response", zlim = c(0.5,1.8),
ticktype = "detailed", border = NA, n.grid = 1000, nticks = 3,
xlab = "m4", ylab = "RR", zlab = "Lambda",
color = "heat", theta= -140, cex.lab = 3, cex.axis = 2.5)Save the plot
# # s4 and RR
# png(filename = here("plots", "04_PVA", "persp_s4_RR_lambda_20211124.png"), width = 1200, height = 772)
# vis.gam(gammod_2_1, view = c("s4", "RR"), plot.type = "persp", type = "response", zlim = c(0.5,1.8),
# ticktype = "detailed", border = NA, n.grid = 1000, nticks = 3,
# xlab = "s4", ylab = "RR", zlab = "Lambda",
# color = "heat", theta= -140, cex.lab = 3, cex.axis = 2.5)
# dev.off()GLM
Response = Lambda
# With interactions between RR and all survival values
mod1_3_1 <- glm(Lambda_sto ~ (s1 + s2 + s3 + s4) + RR,
data = df_sc_mean, na.action = 'na.fail', family=Gamma)
# With interactions between RR and all survival values
mod1_3_2 <- glm(Lambda_sto ~ (m1 + m2 + m3 + m4) + RR,
data = df_sc_mean, na.action = 'na.fail', family=Gamma)##
## Call:
## glm(formula = Lambda_sto ~ (s1 + s2 + s3 + s4) + RR, family = Gamma,
## data = df_sc_mean, na.action = "na.fail")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.174754 -0.010237 -0.002538 0.005698 0.039817
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.870086 0.018618 100.45 <2e-16 ***
## s1 -0.199206 0.012780 -15.59 <2e-16 ***
## s2 -0.170727 0.011390 -14.99 <2e-16 ***
## s3 -0.182280 0.012103 -15.06 <2e-16 ***
## s4 -0.522307 0.010212 -51.15 <2e-16 ***
## RR -0.122401 0.002476 -49.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.000289145)
##
## Null deviance: 1.507876 on 325 degrees of freedom
## Residual deviance: 0.095412 on 320 degrees of freedom
## AIC: -1645.8
##
## Number of Fisher Scoring iterations: 4
## Analysis of Deviance Table
##
## Model: Gamma, link: inverse
##
## Response: Lambda_sto
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 325 1.50788
## s1 1 0.05411 324 1.45377 < 2.2e-16 ***
## s2 1 0.04857 323 1.40520 < 2.2e-16 ***
## s3 1 0.04808 322 1.35712 < 2.2e-16 ***
## s4 1 0.67890 321 0.67822 < 2.2e-16 ***
## RR 1 0.58281 320 0.09541 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# s4 and RR have the highest deviance - they explain the model the most
#dredge(mod1_3_1)
plot(allEffects(mod1_3_1),type='response', ylim = c(1,2)) Save the plot
png(filename = here("plots", "04_PVA", "lambda_effects_plot20211216.png"), width = 1200, height = 772)
plot(allEffects(mod1_3_1),type='response', ylim = c(1,2))
dev.off()## png
## 2
R square R^2= 1-(Residual deviance/Null deviance)
## [1] 0.94
##
## Call:
## glm(formula = Lambda_sto ~ (m1 + m2 + m3 + m4) + RR, family = Gamma,
## data = df_sc_mean, na.action = "na.fail")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.174754 -0.010237 -0.002538 0.005698 0.039817
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.795567 0.005226 152.23 <2e-16 ***
## m1 0.199206 0.012780 15.59 <2e-16 ***
## m2 0.170727 0.011390 14.99 <2e-16 ***
## m3 0.182280 0.012103 15.06 <2e-16 ***
## m4 0.522307 0.010212 51.15 <2e-16 ***
## RR -0.122401 0.002476 -49.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.000289145)
##
## Null deviance: 1.507876 on 325 degrees of freedom
## Residual deviance: 0.095412 on 320 degrees of freedom
## AIC: -1645.8
##
## Number of Fisher Scoring iterations: 4
## Analysis of Deviance Table
##
## Model: Gamma, link: inverse
##
## Response: Lambda_sto
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 325 1.50788
## m1 1 0.05411 324 1.45377 < 2.2e-16 ***
## m2 1 0.04857 323 1.40520 < 2.2e-16 ***
## m3 1 0.04808 322 1.35712 < 2.2e-16 ***
## m4 1 0.67890 321 0.67822 < 2.2e-16 ***
## RR 1 0.58281 320 0.09541 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# s4 and RR have the highest deviance - they explain the model the most
#dredge(mod1_3_2)
plot(allEffects(mod1_3_2),type='response')R square R^2= 1-(Residual deviance/Null deviance)
## [1] 0.94
Model summary
| Unique (#) | Missing (%) | Mean | SD | Min | Median | Max | ||
|---|---|---|---|---|---|---|---|---|
| Run | 326 | 0 | 16525.0 | 10085.5 | 50.5 | 16300.5 | 60150.5 | |
| Year | 207 | 0 | 19.5 | 5.6 | 6.6 | 20.3 | 25.0 | |
| IndAll | 326 | 0 | 830.9 | 473.9 | 21.4 | 1162.3 | 1406.3 | |
| IndB | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndK | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndUb | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndFP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndP | 326 | 0 | 813.2 | 465.2 | 15.6 | 1143.5 | 1386.3 | |
| IndBFP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndBP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndKFP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndKP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndUbFP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndUbP | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| IndJuv | 193 | 0 | 1.0 | 0.4 | 0.7 | 0.9 | 2.6 | |
| IndSub1 | 326 | 0 | 214.3 | 135.0 | 4.8 | 252.5 | 674.8 | |
| IndSub2 | 326 | 0 | 152.1 | 91.8 | 3.5 | 181.6 | 351.3 | |
| IndAdu | 326 | 0 | 463.5 | 266.3 | 12.3 | 576.7 | 787.2 | |
| m1 | 3 | 0 | 0.3 | 0.1 | 0.2 | 0.3 | 0.4 | |
| m2 | 3 | 0 | 0.2 | 0.1 | 0.1 | 0.2 | 0.3 | |
| m3 | 3 | 0 | 0.2 | 0.1 | 0.1 | 0.2 | 0.3 | |
| m4 | 3 | 0 | 0.1 | 0.1 | 0.0 | 0.1 | 0.2 | |
| RR | 6 | 0 | 0.7 | 0.3 | 0.5 | 0.7 | 4.0 | |
| N_Supplements | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Supplement_Time | 1 | 0 | 4.0 | 0.0 | 4.0 | 4.0 | 4.0 | |
| Stoch_Frequency | 1 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Stoch_Severity | 1 | 0 | 0.2 | 0.0 | 0.2 | 0.2 | 0.2 | |
| N_Juveniles | 1 | 0 | 37.0 | 0.0 | 37.0 | 37.0 | 37.0 | |
| N_Subadults1 | 1 | 0 | 11.0 | 0.0 | 11.0 | 11.0 | 11.0 | |
| N_Subadults2 | 1 | 0 | 8.0 | 0.0 | 8.0 | 8.0 | 8.0 | |
| N_Adults | 1 | 0 | 18.0 | 0.0 | 18.0 | 18.0 | 18.0 | |
| Lambda_sto | 326 | 0 | 1.1 | 0.1 | 1.0 | 1.1 | 1.4 | |
| SD_Lambda | 326 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |
| Extinct | 6 | 0 | 0.1 | 1.4 | 0 | 0.0 | 24 | |
| s1 | 3 | 0 | 0.7 | 0.1 | 0.6 | 0.7 | 0.8 | |
| s2 | 3 | 0 | 0.8 | 0.1 | 0.7 | 0.8 | 0.9 | |
| s3 | 3 | 0 | 0.8 | 0.1 | 0.7 | 0.8 | 0.9 | |
| s4 | 3 | 0 | 0.9 | 0.1 | 0.8 | 0.9 | 1.0 | |
| pext | 6 | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.2 |
varnam <- c('s1' = 'Survival of stage 1',
's2' = 'Survival of stage 2',
's3' = 'Survival of stage 3',
's4' = 'Survival of stage 4',
'RR' = 'Reproductive Rate')
varnam2 <- c('m1' = 'Mortality of stage 1',
'm2' = 'Mortality of stage 2',
'm3' = 'Mortality of stage 3',
'm4' = 'Mortality of stage 4',
'RR' = 'Reproductive Rate')
# modelplot(mod1_3,
# coef_omit = 'Interc',
# coef_map = varnam,
# conf_level = .99)
modelplot(mod1_3_1,
coef_omit = 'Interc',
coef_map = varnam,
conf_level = .99) Session Info
## DO NOT REMOVE!
## We store the settings of your computer and the current versions of the
## packages used to allow for reproducibility
Sys.time()## [1] "2022-01-06 18:55:07 CET"
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 22000)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=German_Germany.1252 LC_CTYPE=German_Germany.1252 LC_MONETARY=German_Germany.1252 LC_NUMERIC=C LC_TIME=German_Germany.1252
##
## attached base packages:
## [1] splines stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] forcats_0.5.0 stringr_1.4.0 dplyr_1.0.2 purrr_0.3.4 readr_1.4.0 tidyr_1.1.2 tibble_3.0.3 ggplot2_3.3.2 tidyverse_1.3.0
## [10] pwr_1.3-0 plot3D_1.4 MuMIn_1.43.17 modelsummary_0.6.5 mgcv_1.8-33 nlme_3.1-149 lattice_0.20-41 here_0.1 ggeffects_1.0.0
## [19] gam_1.20 foreach_1.5.1 effects_4.2-0 carData_3.0-4
##
## loaded via a namespace (and not attached):
## [1] minqa_1.2.4 colorspace_1.4-1 ellipsis_0.3.1 showtext_0.9 sjlabelled_1.1.7 rprojroot_1.3-2 estimability_1.3 fs_1.5.0 rstudioapi_0.11
## [10] farver_2.0.3 showtextdb_3.0 remotes_2.2.0 fansi_0.4.1 lubridate_1.7.9 xml2_1.3.2 codetools_0.2-16 knitr_1.30 pkgload_1.1.0
## [19] jsonlite_1.7.1 nloptr_1.2.2.2 broom_0.7.4 dbplyr_1.4.4 compiler_4.0.3 d6_0.1.0.0 httr_1.4.2 backports_1.1.10 assertthat_0.2.1
## [28] Matrix_1.2-18 survey_4.0 cli_2.0.2 htmltools_0.5.0 prettyunits_1.1.1 tools_4.0.3 misc3d_0.9-0 gtable_0.3.0 glue_1.4.2
## [37] tables_0.9.6 tinytex_0.26 Rcpp_1.0.5 cellranger_1.1.0 vctrs_0.3.4 iterators_1.0.13 insight_0.11.1 xfun_0.18 ps_1.4.0
## [46] testthat_2.3.2 lme4_1.1-25 rvest_0.3.6 lifecycle_0.2.0 devtools_2.3.2 statmod_1.4.35 MASS_7.3-53 scales_1.1.1 hms_0.5.3
## [55] yaml_2.2.1 memoise_1.1.0 stringi_1.5.3 highr_0.8 desc_1.2.0 checkmate_2.0.0 boot_1.3-25 pkgbuild_1.1.0 rlang_0.4.7
## [64] pkgconfig_2.0.3 evaluate_0.14 labeling_0.3 processx_3.4.4 tidyselect_1.1.0 magrittr_1.5 bookdown_0.20 R6_2.4.1 generics_0.0.2
## [73] DBI_1.1.0 pillar_1.4.6 haven_2.3.1 withr_2.3.0 survival_3.2-7 nnet_7.3-14 modelr_0.1.8 crayon_1.3.4 utf8_1.1.4
## [82] rmarkdown_2.4 sysfonts_0.8.1 usethis_1.6.3 grid_4.0.3 readxl_1.3.1 blob_1.2.1 callr_3.5.0 rmdformats_0.3.7 webshot_0.5.2
## [91] reprex_0.3.0 digest_0.6.25 stats4_4.0.3 munsell_0.5.0 viridisLite_0.3.0 kableExtra_1.3.1 mitools_2.4 tcltk_4.0.3 sessioninfo_1.1.1